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Cytotoxic T-lymphocytes (CTLs) recognize viral protein fragments displayed by major histocompatibility complex (MHC) molecules on the surface of virally infected cells and generate an anti-viral response that can kill the infected cells.…

We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…

A thermodynamically consistent phase-field model is introduced for simulating multicellular deformation, and aggregation under flow conditions. In particular, a Lennard-Jones type potential is proposed under the phase-field framework for…

We develop a stochastic model to study the specific response of the immune system. The model is based on the dynamical interaction between Regulatory and Effector CD4+ T cells in the presence of Antigen Presenting Cells inside a lymphatic…

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter…

In previous work, we studied host response to a pathogen which uses a cycle of immunologically distinct stages to establish and maintain infection. We showed that for generic parameter values, the system has a unique biologically meaningful…

One of the barriers to the development of effective adoptive cell transfer therapies (ACT), specifically for genetically engineered T-cell receptors (TCRs), and chimeric antigen receptor (CAR) T-cells, is target antigen heterogeneity. It is…

Switching interacting particle systems studied in probability theory are the stochastic processes of hopping particles on a lattice made up of slow and fast particles, where the switching between these types of particles occurs randomly at…

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as…

We have developed a mathematical model for in-host virus dynamics that includes spatial chemotaxis and diffusion across a two dimensional surface representing the vaginal or rectal epithelium at primary HIV infection. A linear stability…

Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…

T lymphocytes (T cells) orchestrate adaptive immune responses upon activation. T cell activation requires sufficiently strong binding of T cell receptors (TCRs) on their surface to short peptides (p) derived from foreign proteins, which are…

An essential feature of the adaptive immune system is the proliferation of antigen-specific lymphocytes during an immune reaction to form a large pool of effector cells. This proliferation must be regulated to ensure an effective response…

Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…

The transmission (T) and reflection (R) coefficients are studied in periodic systems and random systems with gain. For both the periodic electronic tight-binding model and the periodic classical many-layered model, we obtain numerically and…

Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…

Chimeric antigen receptor T cells (CAR T cells) are dosed similarly to donor lymphocyte infusions following hematopoietic cell transplantation. In this perspective paper a mathematical basis for personalized dosing of CAR T cells is…

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…

Quantum integrable systems have very strong mathematical properties that allow an exact description of their energetic spectrum. From the Bethe equations, I formulate the Baxter "T-Q" relation, that is the starting point of two…

Intra-tumour phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources, which is extremely…